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Closed-streamline flows past rotating single cylinders and spheres: inertia effects

Published online by Cambridge University Press:  29 March 2006

G. G. Poe  and
Andreas Acrivos
G. G. Poe
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305 Present address: Aerotherm Division of Acurex Corporation, Mountain View, California 94042.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
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Abstract

The flow around a cylinder and a sphere rotating freely in a simple shear was studied experimentally for moderate values of the shear Reynolds number Re. For a freely rotating cylinder, the data were found to be consistent with the results obtained numerically by Kossack & Acrivos (1974), at least for Reynolds numbers up to about 10. Rates of rotation of a freely suspended sphere were also obtained over the same range of Reynolds numbers and showed that, with increasing Re, the dimensionless angular velocity does not decrease as fast for a sphere as it does for a cylinder. In both cases, photographs of the streamline patterns around the objects were consistent with this behaviour. Furthermore, it was found in each case that the asymptotic solutions for Re [Lt ] 1 derived by Robertson & Acrivos (1970) for a cylinder and by Lin, Peery & Schowalter (1970) for a sphere are not valid for Reynolds numbers greater than about 0.1, and that the flow remains steady only up to values of Re of about 6.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 4 , 23 December 1975 , pp. 605 - 623
Copyright
© 1975 Cambridge University Press

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References

Bretherton, F. P. 1962 Slow viscous motion round a cylinder in a simple shear. J. Fluid Mech. 12, 591.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Cox, R. G., Zia, I. Y. Z. & Mason, S. G. 1968 Particle motions in sheared suspensions. XXV. Streamlines around cylinders and spheres. J. Colloid Interface Sci. 27, 7.Google Scholar
Darabaner, C. L., Raasch, J. K. & Mason, S. G. 1967 Particle motions in sheared suspensions. XX. Circular cylinders. Can. J. Chem. Engng, 45, 3.Google Scholar
Dean, W. R. 1928 Fluid motion in a curved channel. Proc. Roy. Soc. A 121, 402.Google Scholar
Goertler, H. 1940 Über eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden. Nachr. Ges. Wiss. Göttingen, 2, 1.
Goertler, H. 1941 Instabilität laminarer Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen. Z. angew. Math. Mech. 21, 250.Google Scholar
Ho, B. P. & Leal, L. G. 1974 Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365.Google Scholar
Kohlman, D. L. 1963 Experiments on cylinder drag, sphere drag and stability in rectilinear Couette flow. M.I.T. Fluid Dyn. Res. Lab. Rep. no. 63–1.Google Scholar
Kossack, C. A. & Acrivos, A. 1974 Steady simple shear flow past a circular cylinder at moderate Reynolds numbers: a numerical solution. J. Fluid Mech. 66, 353.Google Scholar
Lin, C. C. 1966 The Theory of Hydrodynamic Stability. Cambridge University Press.
Lin, C. J., Peery, J. H. & Schowalter, W. R. 1970 Simple shear flow round a rigid sphere: inertial effects and suspension rheology. J. Fluid Mech. 44, 1.Google Scholar
Poe, G. G. 1975 Closed streamline flows past rotating particles: inertia effects, lateral migration, heat transfer. Ph.D. thesis, Stanford University.
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237.Google Scholar
Raasch, J. K. 1961 Das Verhalten suspendierter Feststoffteilchen in Scherströmungen hoher Zähigkeit. Z. angew. Math. Mech. 41, 147.Google Scholar
Robertson, C. R. 1969 Low Reynolds number shear flow past a rotating circular cylinder: momentum and heat transfer. Ph.D. thesis, Stanford University.
Robertson, C. R. & Acrivos, A. 1970 Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer. J. Fluid Mech. 40, 685.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. A 223, 289.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. Roy. Soc. A 146, 501.Google Scholar
Trevelyan, B. J. & Mason, S. G. 1951 Particle motions in sheared suspensions. I. Rotations. J. Colloid Sci. 6, 354.Google Scholar